A coupled agent-based model for France for simulating adaptation and migration decisions under future coastal flood risk

In this study, we couple an integrated flood damage and agent-based model (ABM) with a gravity model of internal migration and a flood risk module (DYNAMO-M) to project household adaptation and migration decisions under increasing coastal flood risk in France. We ground the agent decision rules in a framework of subjective expected utility theory. This method addresses agent’s bounded rationality related to risk perception and risk aversion and simulates the impact of push, pull, and mooring factors on migration and adaptation decisions. The agents are parameterized using subnational statistics, and the model is calibrated using a household survey on adaptation uptake. Subsequently, the model simulates household adaptation and migration based on increasing coastal flood damage from 2015 until 2080. A medium population growth scenario is used to simulate future population development, and sea level rise (SLR) is assessed for different climate scenarios. The results indicate that SLR can drive migration exceeding 8000 and 10,000 coastal inhabitants for 2080 under the Representative Concentration Pathways 4.5 and 8.5, respectively. Although household adaptation to flood risk strongly impacts projected annual flood damage, its impact on migration decisions is small and falls within the 90% confidence interval of model runs. Projections of coastal migration under SLR are most sensitive to migration costs and coastal flood protection standards, highlighting the need for better characterization of both in modeling exercises. The modeling framework demonstrated in this study can be upscaled to the global scale and function as a platform for a more integrated assessment of SLR-induced migration.

The two coupled models of DYNAMO-M. Household adaptation and migration (within the coastal floodplain -indicated in blue-and to inland departments) is simulated by the ABM. Inland migration between departments (black nodes) and migration towards the coastal floodplain (green nodes) is simulated by a gravity model. HouseholdAgents represent individual households residing in the coastal floodplain, whereas CoastalNodes and InlandNodes represent aggregated households of the subnational administrative unit (s ee section 1.2). This figure was generated using QGIS 3.22.13 (QGIS Association: https://qgis.org/).

1.2.b By what attributes (i.e. state variables and parameters) are these entities characterized?
Each HouseholdAgent is characterized by a geospatial location in the flood zone, which determines their interactions with the environment. A full description of all attributes of a HouseholdAgent is provided in table 1. The HouseholdAgents make decisions based on Subjective Expected Utility Theory (SEUT, see section 3.4 Submodels).
CoastalNodes and InlandNodes contain aggregated information, such population size and the number of households. They also contain an income distribution derived from local census data, a distance matrix of distance to all other nodes, and a dummy variable indicating whether the subnational administrative unit is adjacent to the coast. Migration flows between InlandNodes and towards CoastalNodes are modelled by the gravity model using utility maximization (see section 3.4 Submodels).

1.2.c What are the exogenous factors / drivers of the model?
There are two exogenous drivers in the model: 1) sea level rise, captured by an increase of inundation levels associated with return periods ranging from 2-1,000 years under different climate change scenarios (van Vuuren et al., 2011;Ward et al., 2020), and 2) aggregated population development as projected in the World Population Prospects (United Nations, 2019). For the latter, we only apply one medium population growth scenario. The spatial distribution of household agents is driven by migration processes in the model.

1.2.d If applicable, how is space included in the model?
Space is included as 1x1km2 gridded cells in which households are located and inundation levels are simulated.

1.2.e What are the temporal and spatial resolutions and extents of the model?
The model runs in subnational administrative units and can be implemented at a larger country or regional scale. It simulates household decisions in yearly timesteps spanning 65 years between 2015 and 2080. Inundation maps have a horizontal resolution of 1 square km and a vertical resolution in centimeters. Households moving into the floodplain each calculate the subjective expected utility in a number of randomly selected urban cells within the floodplain based on their risk perception, objective flood risk in the cell, and amenity value. The agents are then allocated in the with the highest subjective expected utility. Then, using annual flood hazards maps, all household agents sample the inundation levels in their current location for flood events with return periods of 2 to 1,000 years. A submodel is then used to simulate stochastic flood events in each subnational administrative unit. These events are assumed to occur independent. This is done by a random draw from data on the different return periods of flood events (see section 3.4, submodels). Agents affected by flooding store the current year in memory, and all agents update their risk perception parameter based on the time passed since they last experienced a flood event. Next the ABM iterates through all HouseholdAgents to calculate the subjective time discounted expected utility of the three behavioral strategies (no action, adapt or migrate). This process is shown in more detail in figure 2.

Gravity model
The gravity model is applied to simulate migration flows between InlandNodes and towards  The modelling approach presented in DYNAMO-M views migration as an alternative adaptation strategy as a response to sea level rise next to flood proofing buildings or 'no adaptation' (Black et al., 2011;Hauer et al., 2020). The choice of which adaptation strategy to apply is shaped not only by increasing flood hazard, but also by economic and political factors, and individual characteristics. In this study we aim to improve the representation of human behavior in flood risk assessment by including economic factors, such as, income differentials and amenity value, together with individual factors, such as, household perceptions of flood risk and risk aversion. We apply an agent-based model to deal with heterogeneity in adaptation behavior considering a dynamic risk perception and heterogeneity in household income and wealth.

2.1.b On what assumptions is/are the agents' decision model(s) based?
Household decisions in DYNAMO-M are grounded in a framework of subjective expected utility theory (Fishburn, 1981;Friedman & Savage, 1948;von Neumann & Morgenstern, 1953). Literature has shown that humans are bounded in their rationality, and act on the limited information available to them (Fishburn, 1981). In the context of flood adaptation, the perception of flood risk often determines whether people invest in flood adaptation measures (Aerts, 2020). Flood risk perception is dynamic over time, with people generally underestimating flood probability in absence of flooding and overestimating flood probability after just having experienced a flood event . To account for this bounded rational behavior, we calculate a subjective expected utility by using a dynamic risk perception parameter that adjusts objective flood risk based on flood ex perience (de Ruig et al., 2022;Fishburn, 1981;Haer et al., 2020;Schrieks et al., 2021).
Subjective Expected utility theory (SEUT) is a well-established framework for simulating adaptation and migration decisions under uncertainty and risk in agent-based models of coupled human-natural systems (Bell et al., 2019;De Koning & Filatova, 2020;de Ruig et al., 2022). SEUT allows for a weighing of different adaptation strategies as a function of wealth and the costs and benefits under each strategy (Schrieks et al., 2021). This framework of SEUT was chosen as it allows for a direct weighing of the three behavioral strategies analyzed in this study, while accounting for bounded rational behavior.

2.1.d If the model / a submodel (e.g. the decision model) is based on empirical data, where does the data come from?
We calibrate the risk perception parameter on survey data from (Poussin et al., 2013). From this data, we use the implementation rate of various floodproofing measures for 885 households in France.

2.1.e At which level of aggregation were the data available?
The survey data of Poussin et al. (2013) is available at the household level.

2.2.a What are the subjects and objects of decision-making? On which level of aggregation is decision-making modeled? Are multiple levels of decision making included?
In DYNAMO-M households make individual decisions to implement dry floodproofing or to migrate to any other node. Only a single level of decision making is included.

2.2.b What is the basic rationality behind agents' decision-making in the model? Do agents pursue an explicit objective or have other success criteria?
Household agents aim to maximize subjective time discounted utility, which is a function of wealth, coastal amenity, flood damages, and the costs of the different adaptation strategies. They reach this goal by either moving or implementing flood damage reducing measures.

2.2c How do agents make their decisions?
Agents in DYNAMO-M make decisions based on subjective expected utility theory. They weight the utility outcomes of no action, staying and implementing dry floodproofing, or migrating to all other nodes. Households choose the strategy with the highest utility outcome.

2.2.d Do the agents adapt their behavior to changing endogenous and exogenous state variables?
And if yes, how?
The only exogenous variable driving household decisions are increasing flood damages under sea level rise. We assume households know the inundation levels in the current timestep and project these into the future to formulate predictions of future risks. Households thus adapt their behavior to changing coastal flood risk. Population development affects the number of household agents in residing in the coastal floodplain, resulting a potential (de-) in-crease of the exposed household population. A larger population, furthermore, increases the migration flow towards the flood zone, as population size has a positive effect on migration flows modeled by the gravity model of migration (see subsection 3.4).

2.2.e Do social norms or cultural values play a role in the decision-making process?
No.

2.2.f Do spatial aspects play a role in the decision process?
Households calculate flood risk based on inundation levels in their current location. Distance between nodes is a factor when calculating the migration costs between nodes.

2.2.g Do temporal aspects play a role in the decision process?
Households apply a decision horizon and a time discounting factor to calculate the subjective time discounted expected utility of each behavioral strategy. Inundation levels increase over time because of sea level rise, affecting the expected utility of decisions involving staying in their current location.

2.2.h To which extent and how is uncertainty included in the agents' decision rules?
We apply an intention to action parameter for agents deciding to migrate to another node (Chabé-Ferret et al., 2018). Using this factor, we randomly sample households that convert their migration intentions to migration action. The stochastic model for simulating random flooding event, account for uncertainty in future flood events.

2.3.b Is collective learning implemented in the model?
No.

2.4.a What endogenous and exogenous state variables are individuals assumed to sense and consider in their decisions? Is the sensing process erroneous?
Households sense changes in coastal flood hazard and know their future income, wealth, and expected coastal amenities when migrating to other nodes based on their current position in the income distribution. Only the sensing of flood risk is erroneous, as it is affected by the risk perception parameter.

2.4.b What state variables of which other individuals can an individual perceive? Is the sensing process erroneous?
Households do not sense the state variables of other individuals.

2.4.c What is the spatial scale of sensing?
Households sense subjective flood risk and coastal amenity value in their current location. Households sense expected wealth, income, and coastal amenities for migration to all other nodes in the model.
Flood risk in destination nodes is currently not sensed by the agent.
2.4.d Are the mechanisms by which agents obtain information modeled explicitly, or are individuals simply assumed to know these variables?
The mechanisms by which agents obtain information are modelled explicitly, sensing only happens locally.

2.4.e Are costs for cognition and costs for gathering information included in the model?
We include migration costs that monetizes the psychological costs of migration. This cost increases with distance between origin and destination node. Although we do not model the cost of gathering information explicitly, distance does constitute to a cognitive cost in evaluating the migration strategy.

2.5.a Which data uses the agent to predict future conditions?
Agents extrapolate the current conditions to make expectations of future conditions in each year within the time horizon.

2.5.b Might agents be erroneous in the prediction process, and how is it implemented?
Predictions of future flood risks are affected by the agent's current risk perception, resulting in under and overestimations of future flood probabilities. Projections of sea level rise are not included in the agents' predictions of future inundation levels.

2.6.a Are interactions among agents and entities assumed as direct or indirect?
Interactions between agents and their environment (flood hazard) are mediated by their risk perception and adaptation status (whether they have implemented dry floodproofing measures). The number of individuals residing in a coastal node affects the number of households moving into the node via the gravity model, as the total population residing in a node is factor in the gravity model of migration.

2.6.b On what do the interactions depend?
Interactions depend on spatial location. Agents sample the inundation levels associated with flooding of different return periods based on their current location. Interactions between the environment are mediated by the agent's risk perception and adaptation status.

2.6.c If the interactions involve communication, how are such communications represented?
Interactions currently do not involve communication.

2.6.d If a coordination network exists, how does it affect the agent behaviour? Is the structure of the network imposed or emergent?
No coordination network exists.

2.7.a Do the individuals form or belong to aggregations that affect, and are affected by, the individuals? Are these aggregations imposed by the modeller or do they emerge during the simulation?
Households residing outside of the coastal flood plain are aggregated in inland nodes. The cumulative household size (total population) affects migration flows projected under the gravity model of migration and affects the size of the migration flow emerging from household decisions in the ABM.
Households residing in the 1/100-year flood zone are embedded in coastal nodes, each representing the coastal flood zone of a NUTS-3 region.

2.7.b How are collectives represented?
These collectives are represented as a different kind of entities in the gravity model (inland and coastal nodes). The collective shares state variables, such as, an income distribution and population size.

2.8.b Are the agents heterogeneous in their decision-making? If yes, which decision models or decision objects differ between the agents?
Decisions in the expected utility framework are a function of agent wealth, coastal amenities, cost of adaptation, and perceived flood risk. The decision to implement dry floodproofing is limited by a budget constraint. This means that the adaptation option is not accessible to low-income households.
1.12 Stochasticity 2.9.a What processes (including initialization) are modeled by assuming they are random or partly random?
During the initialization phase households residing in the floodplain are assigned a random position in the income distribution. In the spin up period used to initialize the agent population we run the model for 15 iterative timesteps whilst simulating random flood events based on flood probabilities. The spatial allocation of households in the coastal node is in part random to prevent all households moving towards the single cell with the highest expected utility. Households that are removed from the coastal node because of natural population decline are selected at random. The procedure for translating migration intentions to migration behavior selects a random subset of households from all households for which migration yields the highest utility outcome.

2.10.a What data are collected from the ABM for testing, understanding, and analyzing it, and how and when are they collected?
The total population of each node, the implementation rate of dry floodproofing measures for each coastal node, the total expected annual flood damages for each coastal node, and migration matrices from all nodes are tracked and exported after each timestep. Optionally all agents and their attributes, such as agent income, experienced amenity value, and location, can be exported each year.

3.1.a How has the model been implemented?
The model is implemented in Python 3.10.6.

3.1.b Is the model accessible and if so where?
Model code and documentation is made publicly available on Github, via https://doi.org/10.5281/zenodo.7057487

3.2.a What is the initial state of the model world, i.e. at time t=0 of a simulation run?
In this section we describe to model application to France. Data sources may vary based on the case study location; however, the procedure remains roughly the same.
Inland and coastal nodes are constructed by overlaying polygon shapefiles of administrative areas with the 1/100-year flood zone of 2080 (GADM, 2022;Ward et al., 2020). For each node, households are sampled using gridded population data from the Global Human Settlement Layer of 2015 (GHSL) (Pesaresi & Freire, 2016). This procedure ensures that the total number of individuals within each node corresponds with the population in 2015. At t=0, a total of 18,233,835 households are aggregated in inland nodes and 77,391 households are embedded in the coastal nodes.
The gravity model is calibrated using migration matrices constructed using survey data on residential mobility (INSEE, 2017a). Income distributions for each node are constructed using income statistics on the department level and assuming a lognormal distribution (INSEE, 2016). A spin up period of 15 years is applied to initiate the adaptation status of agents in the coastal nodes. This spin up period is calibrated using survey data on the implementation rate of dry floodproofing measures in France (Poussin et al., 2013).

3.2.b Is initialization always the same, or is it allowed to vary among simulations?
During the spin-up period of the initialization phase flooding is simulated stochastically. This results in slightly different initial model conditions. When comparing scenarios, the random seed can be fixed, resulting in identical initial conditions.

3.2.c Are the initial values chosen arbitrarily or based on data?
Household income is based on local statistics data of French bureau of statistics (INSEE, 2016).
Household wealth is determined based on the agent position in the income distribution following the factors described in Eurostat (2020). The amenity values are characterized based on the agent's distance to coast and hedonic pricing studies of Conroy & Milosch (2011) and Muriel et al. (2008).
Fixed migration costs are based on (Kennan & Walker, 2011;Ransom, 2022). The lifespan of dry floodproofing set based on (Aerts & Botzen, 2011). The factor converting migration intention to migration behavior is based on findings from Lu (1999). Other input data include gridded population maps to sample the agent population and regional census data to initialize household income.

3.4.a What, in detail, are the submodels that represent the processes listed in 'Process overview and scheduling'?
Submodel 1: Expected utility calculations: The agent executes the strategy yielding the highest subjective time discounted utility (DEU) within its budget constraints. The formulas for calculating the DEU of each strategy are as follows: Utility is a function of household wealth (W), the amenity value of the current household location A x , current household income I x , expected damage D per event i, and adaptation costs C adapt . Additional variables for calculating the DEU of migration are prospected income Inc in destination node y, prospected amenity value in destination node A y , and migration costs C migration to destination node y.
Bounded rationality is captured by risk perception factor β. This perception factor results in both underestimations of flood hazard during periods of no flooding ( β < 1) and overestimations of flood hazard immediately after a flood event (β > 1). Risk perception as a function of the number of years after the most recent flood event, following the equation shown here: = * 1.6 − * + 0.01 Expected wealth states are summed over time horizon T and discounted using discounting factor r.
The household chooses to execute the strategy yielding the highest time discounted subjective utility

DEU.
Submodel 2: Gravity mode of migration Migration between inland nodes and toward coastal nodes is simulated using a gravity-based model of migration (Ramos, 2016). By including a model that simulates migration towards the floodplain, DYNAMO-M allows for studying the effects of changing push and pull factors on coastward migration under scenarios of sea-level rise. This provides a more realistic inflow of households towards the coastal floodplain than is achieved by only accounting for natural population growth. The theorical basis of gravity models of migration is generally represented as a random utility model (Khan et al., 2022;Ramos, 2016;Sheppard, 1978). The gravity model and the ABM are here embedded in a framework of utility maximization based on income differentials and coastal amenity values. Both models simulate migration decisions based on expected utility gains of migrating to another administrative unit.
A full description of this procedure is provided in the accompanying manuscript.

3.4.b What are the model parameters, their dimensions and reference values?
The parameter values can be found in table 2.

3.4.c How were submodels designed or chosen, and how were they parameterized and then tested?
The gravity model of migration is well established modeling framework of simulation migration flows (Anderson, 2011;Backhaus et al., 2015;Ramos, 2016). In this model application the gravity model was calibrated on migration matrixed derived from survey data and applied to simulate continued migration towards the coastal zone. Expected utility theory is a commonly applied decision theory in agent-based models of human environmental interactions and allows for incorporating bounded rational behavior by means of a risk perception parameter.